Question

If A is the Matrix

{ 0 1 0}
{ 0 0 1}
{ p q r}

and I is the unit matrix of order 3, then show that A³=Pl+qA+rA²

Answer 1

To prove that A³ equals pI plus qA plus rA² for the given matrix A and the unit matrix I, one would perform matrix multiplication to show that the indicated relation holds, with the coefficients p, q, and r reflecting the arrangement of the matrix elements in the resulting matrix.

Step-by-step explanation:

The student is tasked with showing that if A is a matrix with elements:
{0 1 0}
{0 0 1}
{p q r}, and I is the unit matrix of order 3, then A3 = pI + qA + rA2.

To prove this, we carry out matrix multiplication step by step to derive A2 and then use the result to find A3. It can be shown through successive multiplication that the resulting matrix has the same structure as the given relation, with appropriate elements corresponding to the coefficients p, q, and r.